Set theory: a first course
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York NY
Cambridge University Press
2016
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| Series: | Cambridge mathematical textbooks
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xii, 250 Seiten Diagramme |
| ISBN: | 9781107120327 |
Staff View
MARC
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Record in the Search Index
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CONTENTS Preface The Greek Alphabet page ix xiii 1 Introduction 1.1 Elementary Set Theory 1.2 Logical Notation 1.3 Predicates and Quantifiers 1.4 A Formal Language for Set Theory 1.5 The Zermelo-Fraenkel Axioms 1 1 6 13 20 23 Set-Building Axioms and Operations The First Six Axioms The Extensionality Axiom The Empty Set Axiom The Subset Axiom The Pairing Axiom The Union Axiom The Power Set Axiom Operations on Sets De Morgan’s Laws for Sets Distributive Laws for Sets 28 28 28 29 29 31 32 34 37 37 38 2 Basic 2.1 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5 2.1.6 2.2 2.2.1 2.2.2 3 Relations and Functions 3.1 Ordered Pairs in Set Theory 3.2 Relations 3.2.1 Operations on Relations 3.2.2 Reflexive, Symmetric, and Transitive Relations 3.2.3 Equivalence Relations and Partitions 41 41 43 45 49 50
Contents 3.3 3.3.1 3.3.2 3.3.3 3.3.4 3.4 3.5 Functions Operations on Functions One-to-One Functions Indexed Sets The Axiom of Choice Order Relations Congruence and Preorder 56 59 62 64 65 69 77 4 The Natural Numbers 4.1 Inductive Sets 4.2 The Recursion Theorem on ω 4.2.1 The Peano Postulates 4.3 Arithmetic on ω 4.4 Order on ω 83 84 88 91 95 102 5 On the Size of Sets 5.1 Finite Sets 5.2 Countable Sets 5.3 Uncountable Sets 5.4 Cardinality 110 112 117 124 129 6 Transfinite Recursion 6.1 Well-Ordering 6.2 Transfinite Recursion Theorem 6.2.1 Using a Set Function 6.2.2 Using a Class Function 142 142 145 146 150 7 The Axiom of Choice (Revisited) 7.1 Zorn’s Lemma 7.1.1 Two Applications of Zorn’s Lemma 7.2 Filters and Ultrafilters 7.2.1 Ideals 7.3 Well-Ordering Theorem 156 157 161 165 168 171 8 Ordinals 8.1 Ordinal Numbers 8.2 Ordinal Recursion and Class Functions 8.3 Ordinal Arithmetic 8.4 The Cumulative Hierarchy 175 175 186 195 201
Contents vii 9 Cardinals 9.1 Cardinal Numbers 9.2 Cardinal Arithmetic 9.3 Closed Unbounded and Stationary Sets 208 208 218 227 Notes References Index of Special Symbols Index 239 241 243 245 |
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| isbn | 9781107120327 |
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| physical | xii, 250 Seiten Diagramme |
| publishDate | 2016 |
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| spelling | Cunningham, Daniel W. Verfasser (DE-588)1026856965 aut Set theory a first course Daniel W. Cunningham, SUNY Buffalo State, NY, USA. New York NY Cambridge University Press 2016 xii, 250 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Cambridge mathematical textbooks Includes bibliographical references and index Set theory Textbooks Mengenlehre (DE-588)4074715-3 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Mengenlehre (DE-588)4074715-3 s DE-604 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029256982&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Set theory a first course |
| title_auth | Set theory a first course |
| title_exact_search | Set theory a first course |
| title_full | Set theory a first course Daniel W. Cunningham, SUNY Buffalo State, NY, USA. |
| title_fullStr | Set theory a first course Daniel W. Cunningham, SUNY Buffalo State, NY, USA. |
| title_full_unstemmed | Set theory a first course Daniel W. Cunningham, SUNY Buffalo State, NY, USA. |
| title_short | Set theory |
| title_sort | set theory a first course |
| title_sub | a first course |
| topic | Set theory Textbooks Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Set theory Textbooks Mengenlehre Einführung |
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